If concepts are not introduced properly, children suffer to learn and understand the concept accurately. Although, there are always some fun ways to make mathematics interesting and easy to understand. One such method is introducing the real-life applications of the concept to the students. 

It will help children better relate to the concept, resulting in better understanding. In this article, we have discussed some real-life applications of tangents and normals for making the concept easy and interesting. 

First, let’s begin by decoding what tangents and normals are. 

Decoding tangents and normal 

Tangents and normals are the features of curves. They are the straight lines used to represent the characteristic features of curves and other related geometrical figures. Examples of geometrical figures, important for tangent and normal, involve circles, parabolas, hyperbolas, ellipses, ovals, etc. 

Tangents and normals are two different lines that are applied together to identify the speed and direction of moving objects. Let’s decode both of the terms individually to get a better idea of the concept. 

What are tangents?

A Tangent is any straight line that externally touches a curve at any specific point, and the tangent goes in the same direction as the curve. In other words, only one tangent will touch a specific point of the curve at one time and will move in the direction of the curve itself. The point where the tangent touches the curve is known as the point of tangency. 

For instance, you are riding your bike on a curvy hill, which is an example of a parabola, at full speed. The curvy hill is the curve required for applying the concept. The tangent line is the direction where the bike is going, and any point that your bike is touching the hill is the point of tangency. Your direction is tangent to the hill, which is in the same direction you are riding your bike since tangents move in the direction of the curve. 

What are normals?

Normal to the curve is any straight line that will pass through the curve and be perpendicular to the tangent, passing through the point of tangency. 

For instance, continuing with a bike example, you wish to know in which direction you are turning your bike on the curvy hill at that specific point. The perpendicular line to your tangent (the direction you are going) will represent the normal. Here, normal will help you understand the change in direction concerning tangents on the hilly road.  

Characteristics of tangents and normal

Now that you have a clear idea of tangent and normal (we hope you have!) Let’s understand some of its important characteristics for better comprehending its applications. The characteristics of tangents and normals are- 

• Tangents and normals are always perpendicular to each other. 
• The straight line will only be called a tangent if there is a normal present perpendicular to it. 
• Tangents and normals are straight lines. Hence they will always be represented using linear equations. 
• Generally, normal passes through the center of the curve, but it can vary according to the situation. 
• There is no limit to points of tangent on the curve. They can be endless. 

Tangents and normal: Some real-life applications 

Tangents and Normals have their application more in the real world than in books. If you are trying to spread the pipelines underground or swinging a merry-round, tangents and normal are profoundly applied there. Some real-life applications of tangent and normal are- 

1. Architecture 

The field of architecture relies heavily on tangents and normals. Designing and creating architectural pieces requires knowledge of intersections, joinery of different parts of buildings, interior designing, spacious layout, sense of lighting, etc. All these elements work best if tangent and normal are applied to them and then designed into the architectural piece. 

2. Force and motion of objects 

Tangents and normals are applied to various areas of physics, such as identifying the force applied and the motion of different objects. Tangent and normal help to identify which direction an object is moving and predict its direction if there is any change in velocity or motion. 

3. Illustrations and computer graphics

Arts & crafts, portraits, and illustrations require tangent and normal for highlighting different aspects of art, adding lighting and shadowing to bring a real look to the illustrations, bringing contrast in different elements of the illustrations, and so on. Tangents and normals are also used to represent the detailing on the surface, creating realistic models or portraits by highlighting correct angles and making background and foreground appealing and easy to differentiate. Computer graphics also use tangent and normal to make the graphics more realistic. 

4. Aerodynamics 

Tangents and normal play a crucial role in the field of aerodynamics. From designing the aircraft and its wings to flying the aircraft, considering the concept of tangent and normal is important. The direction air is moving can impact the movement of aircraft or pressure distribution in the aircraft, hence, to deal with these situations, knowledge and application of tangents and normals are important. 

5. Studying sound waves or water waves 

Tangents and normal are used to study the sound proportion and the direction where the sound wave will travel. They are also useful in assessing the reflection of sound waves and the path it will take to reach the surface. The same concept is applied to water waves. The direction in which waves move and the concept of wave crust or wave trough is studied using tangent and normal. 

6. Medical field 

Another major area where tangent and normal are applied is the medical field. Knowledge of the orientation and structure of different anatomical parts is necessary to conduct and study medical tests such as MRI, CT Scans, etc. Tangents and normal ensures that imaging is done from the right angle and the distortions are minimum in the scans obtained. Additionally, studying cellular samples or different species under a microscope requires proper alignment of the samples for accurate results, which can be done through tangent and normal. 

7. Optics

Tangent and normals are applied to the field of optics to study the processes like reflection, refraction, deviation of light from the surface, etc. The passing of light through the prism and the angle it will form, and in which direction is also determined through tangent and normal. Lens or optic fibers are also designed and applied based on tangent and normal. 

8. Astronomy 

Astronomy is another domain that relies heavily on the application of tangent and normal. To determine the orbital mechanics or celestial coordination, tangent and normal are handy. Additionally, studying how different celestial bodies are organized, their position in space relative to other celestial bodies, and how light travels between different celestial bodies also requires the application of tangent and normal. 

9. Cartography 

Cartography, or the art of making maps, is another important application of tangent and normal. Maps are of different types, such as some representing countries, some representing counties, localities, or even specific streets to reach some specific location. To accurately design the map, organizing and positioning different locations, tangents and normal are important. 

10. Robotics 

A rapidly growing field called robotics also involves the application of tangent and normal. Robots or AI machines require preset programs of orientations, positions, directions, motions, speed, distance, etc. Though to preset these elements, they need to be extensively tested and then applied, which can require the use of tangent and normal. Also, fixing or joining different parts of the robot requires the application of tangent and normal for its accurate functioning and movement. 

Concluding thoughts 

Tangents and normals is a widely used mathematical concept applied in various domains. Understanding the real-life application of the concept will help children better comprehend the concept. Children can also engage in online games and math activities to enhance their knowledge of the mathematical concept. Additionally, the right tips and strategies for studying mathematics alone or with peers can help students get a better hang of the concept. 

Sehjal Goel

I am Sehjal Goel, a psychology student, and a writer. I am currently pursuing my Masters’s from Banaras Hindu University, Varanasi. Child psychology has always fascinated me and I have a deep interest in learning about disabilities in children and spreading awareness regarding the same. My other areas of interest are neuropsychology and cognitive psychology. Connect me on Linkedin

The post 10 Common Applications Of Tangents and Normal in Real-life appeared first on Number Dyslexia.

Logarithms have been used for years and have reinforced various scientific discoveries over time. From early astronomical experiments to developing the first data storage device, concepts of exponents and logarithms are widely applied. Considering the same significance of the concept, in this article, we will cover some major real-life applications of logarithms. 

Let’s get started! 

Understanding the concept of Logarithms 

Logarithms is one of the oldest mathematical concepts that made various early scientific and mathematical discoveries possible. The history of logarithms dates back to the 17th century when a Scottish mathematician John Napier invented the concept of logarithms. He coined the term from the Greek words ‘logos’ and ‘arithmos’, which means ‘ratio’ and ‘number’. 

Logarithms is a method to represent a significantly large mathematical value, and it helps to identify how many times a number has to be multiplied to get a desired other number. Logarithms are represented as a base number and power to that base number, using the equation logₕ a=y. 

Let’s understand logarithms using an example. 

Suppose you are a biologist interested in a rare species of bacteria. During your study, you noticed this rare form of bacteria’s population, which is 100, currently, increases at least ten times in an hour. You are interested in finding out how long it will take for the population to reach 10,000. Using logarithms, you can form the equation and find the required time. 

logₕ a=y

Log₁₀ 100 = y 

Here, ‘y’ will be the required time, ‘h’ is the rate of increment in population, and ‘a’ is the current population. The value of ‘y’ can be easily found with the help of the ‘log table’.

Application of logarithms in real-life  

Logarithms form a base of various scientific and mathematical procedures. Logarithms have wide practicality in solving calculus, statistics problems, calculating compound interest, measuring elasticity, performing astronomical calculations, assessing reaction rates, and whatnot. This article will cover some of the most common real-life applications of logarithms. The applications are- 

1. Measuring the sound intensity 

Sounds are measured using a scientific scale called the decibel scale, which works on the principle of logarithms. The scale can measure the faintest whispers and loudest of noises easily and accurately. Further, the decibel scale measures the different intensities of sounds by keeping the normal intensity of the sound as a reference point.

The sound above, below, and on the reference point are all accurately captured by the decibel scale. For instance, 5 times higher than normal intensity sound will be 5db on the decibel scale. 

2. Stock market analysis 

The ups and downs of the stock market require a lot of calculations and predictions, generally based on highly large values and calculations. The data obtained in the stock market are generally expressed in exponential form. Applying and understanding the exponential form of data in every situation is impossible.

Hence it is converted into logarithms for better understanding. Data transformation and normalization during stock market analysis are also carried out using the multiplicative properties of logarithms. 

3. Studying the process of decay of radioactive elements 

Another great application of logarithms in real life is studying the exponential decay process of radioactive elements. The decay of radioactive elements varies to a wide range, from a few seconds to decades. Examples of Exponential decay and growth both utilize the use of logarithms.

Logarithms help to study the half-life of radioactive elements and assess the decay rate and other processes related to radioactive elements, such as medical imaging. 

4. Radiocarbon dating 

Radiocarbon dating is the process of studying the age of geological and archaeological objects infused with radioactive carbon isotopes (C-14) in organic matter. This process helps to identify how old an object is and how long it could have been preserved without decaying and provides an insight into a human’s history timeline. Logarithms here help to convert complex exponential decay equations into simple linear equations for a better understanding of laymen and professionals. 

5. Assessing the magnitude of earthquakes using the Richter scale

Richter scale is a scale widely used for assessing the magnitude of earthquakes by studying the disturbances in the plates of the earth’s layers. This scale works on the principle of logarithms. The energy released from the seismic waves is generally very high in intensity, requiring exponential equations to represent it.

Also, comparing the magnitude of two or more two earthquakes requires logarithms to solve the complex exponential equations. Logarithms simplify the representation and understanding of complex and large exponential values, resulting in better application of the obtained information.  

6. Measuring pH levels of chemicals 

Logarithms are widely applied in the process where studying pH level is important. pH levels help to identify the acidic and alkaline nature of the substances, such as soil, chemical elements, etc. pH levels can be studied through a pH scale that works based on the concept of logarithms.

The PH scale helps determine the concentration of hydrogen ions in the elements or substances and the application of Hydrogen ion-infused elements in various chemical and environmental processes. 

7. Calculating the growth of the human species or other living species 

Logarithms are also applied in the biological field for assessing and calculating the growth of human species and other living species, generally calculated in exponential form. Logarithms come in handy in studying the exponential growth of populations, the speed of doubling the population, comparing the growth rate of two populations predicting the future growth or decline rate of the population, and aiding in studies related to environment and biodiversity. 

Studying human populations using logarithms helps in better planning and making policies for the welfare of the citizens, whereas studying bacteria or other living species populations is useful for understanding their life cycles and processes. 

8. Data compression 

Ever wondered how such large data obtained from various organizations and governments is stored and used? Storing such large data requires various storage devices, which will still be insufficient. In that case, the data compression technique is used, which uses logarithms to simplify and compress the data.

The data is compressed using different coding processes, such as arithmetic, transform, Huffman, Delta, entropy, Shannon-Fano, run-length encoding, etc., based on logarithm and its application.  

9. Analyzing drug concentrations in medicines 

Pharmacology and pharmacokinetics also have major applications of logarithms in identifying drug concentration in medicines and regulating the use of drugs. Logarithms are also used to study the change in the concentration of drugs in the human body over time.

Further, logarithms help to assess how long the drug will stay in the human body and when the effects will wear off. Whether the drug is distributed equally in the whole body or not is also studied through logarithms. 

10. Sensation and perception 

Another important area where logarithms are used is in the scientific study of sensation and perception using the highly renowned Weber’s and Steven’s power laws. Psychophysics and signal detection theory (SDT) also require the application of logarithms to estimate the presence or absence of stimulus and the intensity of the stimulus present. Identifying the magnitude of stimulus and sensory adaptation requires logarithmic scaling. 

Concluding thoughts 

Logarithms is a highly used mathematical concept that makes the findings, representation, and interpretation of data from various disciplines easy and convenient. Understanding and applying logarithms in real life makes various complex processes easy to understand. Solving logarithmic equations is a discovery learning activity that helps discover and predict various phenomena. 

Sehjal Goel

I am Sehjal Goel, a psychology student, and a writer. I am currently pursuing my Masters’s from Banaras Hindu University, Varanasi. Child psychology has always fascinated me and I have a deep interest in learning about disabilities in children and spreading awareness regarding the same. My other areas of interest are neuropsychology and cognitive psychology. Connect me on Linkedin

The post 10 Common Applications Of Logarithms In Real-life appeared first on Number Dyslexia.

One of the key features of differential equations is that they can account for the many factors that can influence the variable being studied. In the field of engineering, differential equations are commonly used to design and analyze systems such as electrical circuits, mechanical systems, and control systems. In the natural sciences, differential equations are used to model the evolution of physical systems over time.

Overall, differential equations play a vital role in our understanding of the world around us, and they are a powerful tool for predicting and controlling the behavior of complex systems. Summarized below are some crucial and common applications of the differential equation from real-life.

Applications of differential equations

Mathematics has grown increasingly lengthy hands in every core aspect. Differential equations have aided the development of several fields of study. 

Hence, just like quadratic equations, even differential equations have a multitude of real-world applications. Some of the most common and practical uses are discussed below.

1. Bonds between atoms and molecules

Everything we touch, use, and see comprises atoms and molecules. In actuality, the atoms and molecules form chemical connections within themselves that aid in maintaining their cohesiveness. 

Atoms are held together by chemical bonds to form compounds and molecules. Covalent, polar covalent, and ionic connections are all types of chemical bonding. The second-order differential equations are used to express them. This equation comes in handy to distinguish between the adhesion of atoms and molecules.

2. Systems of the electric circuit

The absolute necessity is lighted in the dark and fans in the heat, along with some entertainment options like television and a cellphone charger, to mention a few. But how do they function? Electric circuits are used to supply electricity. 

The differential equation of the same type determines a circuit consisting of an inductance L or capacitor C and resistor R with current and voltage variables. The differential equation is regarded as conventional when its second order, reflects the derivatives involved and is equal to the number of energy-storing components used.

3. Population growth

Recording the population growth rate is necessary since populations are growing worldwide daily. We thus take into account the most straightforward differential equations model available to control a particular species’ population dynamics. 

The equation will give the population at any future period. Even though it does not consider numerous variables like immigration and emigration, which can cause human populations to increase or decrease, it proved to be a very reliable population predictor.

4. To describe the motion of pendulums

Every home has wall clocks that continuously display the time. Have you ever observed a pendulum that swings back and forth constantly without pausing? If so, how would you characterize the motion?

Newton’s second law of motion is used to describe the motion of the pendulum from which a differential equation of second order is obtained. Forces acting on the pendulum include the weight (mg) acting vertically downward and the Tension (T) in the string. 

T = mg cos θ

When a pendulum is displaced sideways from its equilibrium position, there is a restoring force due to gravity that causes it to accelerate back to its equilibrium position. This restoring force causes an oscillatory motion in the pendulum.  

Restoring force = m.d²x/dt² = -mg sin θ

5. Exponential growth of bacteria

Microorganisms known as bacteria are so tiny in size that they can only be observed under a microscope. They are present in the air, soil, and water. Surprisingly, they are even present in large numbers in the human body. Some make us healthy, while others make us sick. 

As is often said, nothing in excess is inherently desirable, and the same is true with bacteria. But differential equations assist us similarly when trying to detect bacterial growth.

6. To find the Velocity and Acceleration 

Differential equations can be used to describe the relationship between velocity and acceleration, as well as other physical quantities. For example, Newton’s second law of motion states that the acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. This relationship can be written as a differential equation in the form:

F = ma

where F is the force acting on the object, m is its mass, and a is its acceleration. By solving this differential equation, we can determine the acceleration of an object as a function of time, given the forces acting on it and its mass.

Similarly, we can use differential equations to describe the relationship between velocity and acceleration. For example, the relationship between velocity and acceleration can be described by the equation:

a = dv/dt 

Which forms the above equation as

F = m.dv/dt

where a is the acceleration, v is the velocity, and t is time. By solving this differential equation, we can determine the velocity of an object as a function of time, given its acceleration.

In general, differential equations are a powerful tool for describing and analyzing the behavior of physical systems that change over time, and they are widely used in a variety of fields, including physics, engineering, and economics.

7. To determine radioactivity decay

Differential equations can be used to describe the rate of decay of radioactive isotopes. Radioactive decay is a random process, but the overall rate of decay for a large number of atoms is predictable. The rate of decay for a particular isotope can be described by the differential equation:

dN/dt = -λN

where N is the number of atoms of the isotope at time t, and λ is the decay constant, which is characteristic of the particular isotope. The negative sign in this equation indicates that the number of atoms decreases with time as the isotope decays.

By solving this differential equation, we can determine the number of atoms of the isotope remaining at any time t, given the initial number of atoms and the decay constant. This is useful for predicting the behavior of radioactive isotopes and understanding their role in various applications, such as medicine and power generation.

Strategies to teach differential equations effectively

The task for the lecturer is to create a link between abstract mathematical ideas and real-world applications of the theory. Finding the ideal balance between a grasp of mathematics and its applications in one’s particular subject is essential for successfully teaching a particular concept. 

Since many real-world applications employ differential equations as mathematical models, a course on ordinary differential equations works rather well to put this constructing the bridge idea into practice.

Innovative strategies are needed to raise student engagement and performance in mathematics classrooms. Various strategies that have proved to be effective are as follows:

1. Technology

Technology can be used in various ways, depending on institutional restrictions, available resources, and instructor preferences, such as a teacher-led demonstration tool, a lab activity carried out outside of class time, or an integrated component of regular class sessions. 

2. Modelling Process

Students must translate an issue from a real-world situation into a mathematical model, solve that model, and then apply the solutions to the original problem. Students are asked to create the equation or the model’s heuristics rather than being given the model or algorithm and instructed to enter numbers into the equation to discover the solution. To create a model, it is crucial to define variables with the correct units, state what is known, make reliable assumptions, and identify the problem at hand.

3. Student & feedback

Positive student feedback has been helpful in encouraging students. When students can use their math skills to solve issues they could see again in a scientific or engineering course, they are more likely to acquire the material. According to course-ending polls, students undergo a metamorphosis once they perceive that the lectures and evaluations are focused on issues they could face in the real world. Students believe that the lessons are more engaging. 

Additionally, they think that when they apply mathematics to real-world issues, their confidence levels increase because they can feel if the solution makes sense. They realize that reasoning abilities are just as crucial as analytical abilities. They can get some credit for describing what their intuition tells them should be the solution if they are sure in their model and get an answer that just does not make sense.

Conclusion

Due in part to growing interest in dynamical systems and a general desire to enhance mathematics learning and instruction, the teaching and learning of differential equations are moving in new directions.

The use of technology, which requires that ideas and approaches be approached graphically, numerically, analytically, and descriptively, modeling, and student feedback is a springboard for considering new techniques for helping students understand the fundamental concepts and approaches in differential equations.

Research into students’ thinking and reasoning is producing fresh insights into establishing and maintaining learning settings where students may develop a profound comprehension of mathematical ideas and procedures, in addition to novel pedagogical tactics.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post 7 Real-World Applications Of Differential Equations appeared first on Number Dyslexia.

However, when budding learners identify angles around them, grasping and identifying obtuse angles might not be a tricky affair for them anymore. Therefore, through this blog post, we will try to exhibit various real-life examples of obtuse angles. Furthermore, kids will also understand that angles affect many spheres of our lives. Ultimately, identifying and relating with this angle would no longer be an uphill battle for them. 

Can obtuse angles be seen in real life? Some practical examples explored

Angles are formed by the coinciding of two lines. The intersection point is known as the vertex of the angle. And when the degree measured at or near the vertex is between 90° and 180°, it is called an obtuse angle. At the same time, just like the right angle can be seen in the world around us, the obtuse angle, too, affects many spheres of our lives. Some of these are listed below. 

1. The angle formed by the screen of an open laptop

If you are reading this blog on a laptop, can you tell what the angle formed by the screen, considering that you have put it in a way to help you read facilely? Mostly, whenever we open the screens of our laptops, we always keep it more than 90 degrees, as it helps us see the text and other things clearly, and use the laptop more optimally. Hence, the opened screen, connected to the keyboard part, gives an obtuse angle at the vertex, which is the hinge of the laptop in this case.

2. Sloping rooftops

A sloping rooftop can be seen at places where it rains or snows heavily. Architecturally, these rooftops help the water and snow slide down to the ground so that it does not accumulate on the top of the ceiling, thereby causing damage to the house or building. Hence, the angle formed by the pitched rooftops is always obtuse, so that the snow and rain can directly free fall. This also provides the building or the house with high stability.

3. Recliners

Recliners are commonly seen in movie theatres, homes, and other places have a special feature of the backrest of it going back to help you relax and unwind. However, when you see the angle formed by the perfect recliner that helps you support your back muscles, it is always obtuse as it goes way back to a right angle, that is, 90 degrees. However, if a 180-degree angle is formed, it will be just like a bed. Therefore, a good recliner is one that forms an obtuse angle, providing you with excellent lumbar support.

4. Kids’ slides

When you venture outdoors, try searching for objects that are not perpendicular but a little more than that. Just like a kid’s slide. The ladder part and the side part intersect each other in a way to form a not-so-steep slide for the little ones. This gives the look of an obtuse angle from both sides. Just imagine, if the slide had been perpendicular to the ladder, the slide would have become way too steep, and the chances of kids getting hurt would have been too much. However, to make the slide safer for kids, the sliding part of the swing is often at a larger angle, thus forming an obtuse angle.

5. Various English alphabets

The English alphabet doesn’t just aid us in teaching the language and forming the words. If looked at closely, some alphabets form various angles. For example, the letters X, K, and Y have a noticeable obtuse angle. In the alphabet X and Y, the obtuse angle is present towards the right and the left side of the alphabet. At the same time, in the letter K, an obtuse angle of more than 90 degrees can be seen on the right side. 

6. A door wide opened

Ever seen a door open and wondered what angle it is forming? While most doors open up to a maximum of 90 degrees, forming a right angle due to the wall present at the back. However, in some places, the wall is far back, and when the door is pushed a little harder, it can form an angle of more than 90 degrees, but less than 180 degrees, giving us a clear display of an obtuse angle.

7. Pair of scissors

A pair of scissors, when open, can give us a lot of angles, from right angle to acute to even obtuse. When the scissor is fully open, it forms an angle of a little over 90 degrees. Hence, this clearly displays an obtuse angle.

8. A coat hanger

Ever closely seen the little hanger that holds the weight of all your clothes? This classic coat hanger always comes with a hook, from which two wires pass to form the base of the hanger, which allows you to hang your clothes. The angle formed here near the hanger’s hook is obtuse as it is always more than 90° and less than 180°. The reason behind it is also scientific and logical; if the angle were less than 90, or even 90, the coats, jackets, and all the items that you could hang would just slip off. Hence, a wider obtuse angle is used to ensure great support.

9. Hands of a clock

The hands of a clock, at different times, give us different angles. When the clock strikes 3, 3:30, 6:45, or 9, the hands are at a 90-degree angle, giving us a portrayal of a right angle. At the same time, when the clock strikes 10:30, 12:40, or 1:25,  the angle between the hour hand and the minute hand is clearly more than 90° and less than 180°. Hence it forms an obtuse angle.

10. Angular Bay Windows

A bay window is one that has glass windows on three sides. However, the 2 windows on the side are not perpendicular but form a specific angle. Many times, this angle formed is an obtuse angle. Mostly, these angular bay windows are added to add up to the beauty of the house. The projection of these windows can be an octagon or hexagon, and in this case, the windows at the vertex of the intersection form an obtuse angle. Simply put, an obtuse angle can be seen at the point from which the bay window panels connect. 

Obtuse angle: Tricks that can make these dull angles easier to understand

As we know, the obtuse angle is the one that is larger than a right angle but smaller in degree than a 180-degree straight line. These angles are also called dull angles.

An interesting fact about this angle that can be told to the kids to help them relate between angles and the different triangles is that a scalene and isosceles triangle always has obtuse angles at the vertex of the triangle.

Furthermore, to make these far-reaching concepts more facile for kids, especially the little learners who are having a tough time understanding these angles, including the obtuse angle, the teachers and parents can bring in some funny yet interesting strategies to help them learn it. As we all made up a sentence for learning the order of the planets by repeating My Very Excellent Mother Just Served Us Nine Pizzas, representing Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto. Similarly, we can introduce a strategy to help kids learn these different yet perplexing angles. 

For example, acute angles can be learned as “cute angles” as these are perpetually smaller, hence, cuter looking. On the other hand, the right angle is in a perfect shape; hence they are the “right” angle. Meanwhile, the obtuse angle can be remembered by correlating the word. “Obese angle,” meaning fat or wide. This will help the students remember the angles and the properties associated with them more easily. 

Summing up

As educators and parents, we often have to come up with fun and interesting ways to help budding learners learn the concept in an interesting manner, one which can actually help them retain the topic for longer. Thus, explaining the concepts by giving some real-life examples can act in favor of the little kids, as they can now form a habit of looking for some specimens and instances by themselves. A great way would also be for teachers to give this as an assignment to kids to find real-life examples of the angles around them.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post 10 Common Examples Of Obtuse Angle In Real Life appeared first on Number Dyslexia.

Before we explore real-life examples, let us understand the attributes of a square. 

A square is a two-dimensional shape. It is a four-sided polygon with four equal sides, four equal angles, and four vertices. 

Basic Properties of a Square – 

Here are the following properties that give a square its unique shape – 

• Opposite sides of a square are parallel to each other 
• All four angles are right angles (90 degrees)
• The sum of all interior angles of a square equals 360 degrees
• A square has two equal diagonals 
• The diagonals of a square intersect each other at right angles i.e., 90 degrees

Now that we have discussed the basics of a square, let’s look at some of its real-life examples.

Examples of Squares in real life: 15 commonly-found objects

The square shape appears in many everyday items we see and use on a daily basis. Take a moment to think about how many you can come up with before going through the list below.

1. Chessboard

The most striking feature of a chessboard is its black and white sections. These sections are nothing but squares. The square-shaped sections are colored black and white to form a unique board for the game of chess. You can find a total of sixty-four squares on a chessboard arranged in eight rows and eight columns. 

2. Tiles

Square tiles are amongst the most common tiles used in construction. As tiles are versatile, you can find them in flooring, bathrooms, and kitchen. Square tiles make a good choice in construction as you can easily calculate how many tiles you will need to cover a particular area. When used, they impart a sleek and uniform look to a room.

3. Books

It is common to find books in rectangular shapes. But, take a stroll in a bookstore, and you will find several square-shaped books as well. Especially those tiny little books that easily fit into the hands of babies and toddlers. Board books for little kids are often square and contain specific information on each page. The books often come in bundles and are easy to store and carry because of their small size and square shape.

4. Picture Frames

Square picture frames are another real-life example of squares. They accentuate the overall look of a room by imparting depth to the elements in the frame and making them look more visually appealing. Square picture frames work well with images that highlight a single element. Make a wall collage of your favorite pictures and admire the beauty this basic geometric shape imparts to your living space.

5. Keyboard Keys

Did you ever notice that the keys on your keyboard are also square? In our professional or personal lives, we use keyboards nearly every day. But often, we miss noticing these tiny details even though they are right in front of us. With the advent of the digital world, we have been using our keyboards more than ever. And its square keys provide us a comfortable typing experience.

6. Food Items

Many food items that we relish during our meals or snack times are also squares. For instance, a slice of bread, a brick of a chocolate bar, brownies, and waffles. Interestingly, shapes affect how we perceive things around us. As we always imagine a slice of bread in a square shape, we may find it odd if a triangular-shaped bread is served to us. 

7. Watch/ Wall Clock

Watches and wall clocks are other everyday objects found in a square shape. Be it a regular dial watch or a smartwatch, you can find it either in a circular shape or as a square. Even wall clocks are designed in this shape. The choice, however, depends on the user as some like circular watches and clocks while others prefer square ones.

8. Post-it Notes

Those colorful little notes we love to use to leave notes on the door of our fridge or for official reminders are also squares. These small squares have sufficient space to write quick notes and are easy to use. You would be surprised to know that some artists use these square post-it notes to make striking wall art. Do a quick search on the Internet and see for yourself!

9. Paper Napkins

Disposable paper napkins used in parties and dinners to absorb spills and clean up messes are also square-shaped. If you open a neatly folded napkin, you will reveal a big square consisting of four small squares. 

10. Origami Paper

Origami is the art of folding paper to make interesting things. Making origami crafts with regular paper is a bit difficult due to its thickness. So, people use special origami paper to make origami crafts. Though origami paper is available in different sizes, the most common is square paper which is 20 cm x 20 cm in size. 

11. Crossword Puzzle

A crossword puzzle is a clear example of the utilization of a square shape. It consists of a large square with numerous small squares that contain numbers to help you answer the questions. Solve a round of crossword puzzles if you wish to improve your vocabulary and speed up your thinking ability. 

12. Logos

Logos play a significant role in creating and establishing a brand. And many well-known companies in the world have a square logo. Can you think of some? To highlight a few, we have companies like LEGO, Microsoft, BBC, and GAP, who chose to design their logos in a square format. As a square-shaped logo reflects a strong and professional image, it is preferred by many organizations. 

13. Cushions

If you take a look at the cushions lying on your couch or your bed, you will most probably find them to be square-shaped. Nowadays, you can find cushions in different shapes like a rectangle, circles, or even cloud-shaped cushions for a nursery, but the old-time favorites are the square ones.

14. Pizza Box

Next time you order a pizza, check out its box. It is also a square. The square box conveniently holds the pizza in place so it can be delivered safely and on time. Try not to throw away the box and find ways to recycle it into cute wall art or turn it into your cat’s bed!

15. Carrom Board

Carrom is another game that has a large square board. Its square shape is precisely divided to allow four players to enjoy the game. The game is quite popular in Southeast Asian countries but has gained significant popularity in other countries as well.

Concluding thoughts

The world around us is filled with objects of different shapes. Therefore, it is imperative to have their knowledge for quick identification. Keeping this in mind, shapes are the first few things taught to little children once they are ready to learn.

Through this article, you have seen that many everyday items have a square shape. Square is a preferred shape because of its practicality and symmetry. Because of this, it is widely used in construction, art, food, and many other fields.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post 15 Common Examples Of Squares In Real Life appeared first on Number Dyslexia.

We all have encountered situations wherein measuring the area and perimeter is crucial but when it comes to learning such a concept, it can be challenging due to certain reasons such as using the right units of measurement, confusion between area and perimeter^[1], and learning and applying the right formula for calculation.

Considering this, Teaching such crucial math concepts with the help of real-world applications can contribute to their concept retention ability along with enhancing problem-solving and analytical thinking skills^[2]. Hence, this post outlines various applications of the concept of “area and perimeter” in real life. 

Importance of area and perimeter

Area and perimeter are often confusing for students as these are related to each other and deal with the same field of study. To clearly differentiate between the two, it is crucial to first make a note of their different uses.

Determining area is essential because it helps us understand how much space we need for certain things or activities such as housing, gardening, or parking. It also helps us determine whether a place has enough resources like food and water, which are required for survival.

On the other hand, the perimeter is essential because it helps us determine whether a place has enough room for certain activities such as playing games and running around without bumping into other people/things; it also helps us understand how long it takes for someone to walk from one point to another without getting lost along the way (unless you’re using GPS).

Applications of area and perimeter in daily life

Learning about real-world applications allows students to connect with their environment and interpret the usage of mathematical concepts. Also, knowing these applications helps them find different ways to solve related real-life problems that further enhance their reasoning and problem-solving skills. Given below are some of the important examples and applications of “area and perimeter” in our day-to-day life.

1. Measurement of land or fields:

To protect the field from animals, farmers fence their fields. Also, you must have noticed the boundaries of the park are cemented. For such instances, the perimeter finds its usage.

On the other hand, the area is calculated during the buying and selling of the land in any shape it is. Residential areas are calculated in square feet and agricultural land is calculated in acres.

2. Construction of homes and buildings:

Another important real-life application of area and perimeter is its usage in determining the geometrical aspects of homes and buildings before and during construction. The room you are seated in has an area and perimeter and has been designed carefully with precise measurements. Similarly, all the rooms are combined to contribute to a broad area and perimeter. 

3. Construction of roads and Bridges

A well-constructed and smooth road is every commuter’s dream. To make this dream come true, a lot is required. Besides having good quality raw material, it is essential that proper planning and survey is carried out. The survey also includes the dimensions and geometrical aspects, such as the area and perimeter of the road. 

Similarly, building bridges also requires a lot of planning and surveying. The area and perimeter values of essential points help maintain bridges’ symmetry, which is extremely important to prevent the breakage of bridges. 

4. Determining the material required

While adding tiles of certain dimensions in a room of certain dimensions, or estimating the paint required for a wall, the area is calculated. 

On the other hand, by adding doors, fence, and cabin glasses for the boundary, the perimeter is calculated. Also, while installing tents, the pipes are used to mark the boundaries which are measured with the help of the perimeter.

5. Measuring orbits and planetary motions

For a long time, astronomers have been measuring the distance between planets, their orbitary motions, and much more. The use of area and perimeter in this field has served as the basis for several laws and theorems. 

6. Computer graphics

Pictorial and audio-visual representations of objects have become an essential part of several industries, including entertainment and education. These pictorial and audio-visual representations must be precise and require the aid of area and perimeter. The gaming industry also extensively uses area and perimeter to ensure the graphics are accurate and keep the gamers hooked. 

7. Art and Fashion

An exciting use of area and perimeter is found in the world of art. It is not limited only to painting and sketching but opens doors to the world of apparel designing and accessories. It is self-explanatory how area and perimeter are essential in the world of fashion. Similarly, in the art world, painters and designers must be accurate with their brush strokes. 

Benefits of studying area and perimeter

Area and perimeter have everyday occurrences and practical applications. Besides, the following are the benefits of understanding these concepts clearly. 

1. Studying area and perimeter thoroughly forms one of the most important fundamental concepts. They help students develop their analytical thinking skills, logical reasoning skills, problem-solving methodology, and deductive reasoning abilities. An all-over development like this enhances the holistic growth of the students.  
2. Area and perimeter allow students to map the area and boundary of various regions, thus allowing for the cultivation of the ability to be practically and logically conclusive. 
3. The concepts of area and perimeter find several applications in the real world. They help us decide which materials to use and which design is best suited for construction purposes. Hence, students aspiring to be civil and structural engineers and architects must thoroughly understand these concepts.

Understanding the concepts of area and perimeter with games

Math can be fun, but not for everybody. We understand and embrace the fact that every child has different learning abilities. However, we cannot rule out that concepts such as area and perimeter are of prime importance for students. 

So, we thought of a fun way to help you teach your kids all about area and perimeter. And what can be more fun than learning through games? So let’s find out!

1. Decorate your classroom

The activity is simple and easy to carry out. Since some kids may have trouble remembering the difference between area and perimeter, visual aids can come to their rescue. Studies have shown that visual aids are an effective way to enhance comprehension and retention ability among students. 

For this game, you have to provide your students with cutouts shaped as ‘area’ and ‘perimeter’ and ask them to paste them on objects in the classroom. 

For example, ask them to paste ‘perimeter’ at the boundaries of the black/whiteboard and ‘area’ within the boundaries of the board. In this way, every time they pass the black/whiteboards, they will see the two and hence, slowly retain the information. 

2. The Drawing graph

Provide students with graph sheets and ask them to sketch themselves along the lines in the graph sheet. Once done, ask them to determine the perimeter of their figures. While the perimeter may be easy to determine, for the area, ask them to divide the figure into sub-figures and then determine the area individually for each figure. Later on, they must add all the areas obtained to find the area of the big picture!

3. The Scavenger hunt

Kids love to engage in mind-boggling activities such as scavenger hunts. There are several ways to flag off a scavenger hunt. 

For area, you could tape shapes on the floor and ask students to use the tiles to determine the value. For perimeter, you could hang various shapes around the classroom or corridor and ask students to solve and find the value. 

Conclusion

Area and perimeter are fundamental concepts in geometry that students need to apply both in and outside the classroom in different real-life scenarios. The ability to use these skills effectively can help students solve problems and make decisions in a variety of situations. 

To help students get a hang of this concept, we can make use of interactive alternatives to traditional teaching as it engages students and promotes effective learning. Apart from using real-world applications given above, activities and board games can be employed!

References:

1. Machaba, F. M. (2016, January 1). The concepts of area and perimeter : insights and misconceptions of Grade 10 learners : original research. https://journals.co.za/doi/abs/10.4102/pythagoras.v37i1.304
2. Karakoç, G., & Alacacı, C. (2015). Real world connections in high school mathematics curriculum and teaching. Turkish Journal of Computer and Mathematics Education, 6(1), 31-46

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post 7 Common Applications Of Area And Perimeter In Daily Life appeared first on Number Dyslexia.

A quadratic equation is an equation containing variables, among which at least one must be squared. It is expressed in the following form:

ax²+bx+c= 0

Here, ‘x’ is the unknown value we need to calculate. The letters ‘a’ and ‘b’ represent the known numbers you put in while calculating. However, one must remember that ‘a’ can never be zero. 

Although simply looking at the equation you may feel that it is not something you use very often. So, let us give you a few examples of how quadratic equations find their application in our daily lives.

Real-life applications of quadratic equations

1. Building a home? How do you calculate areas?

Constructors and architects take the help of quadratic equations to develop a building. For any building, you need to calculate how much land you have, how big each room will be, what the shape of the building will be, etc.

So, if you are building a rectangular house, you know one side of the house will be bigger than the other. So, you can use the ratio of these two sides to calculate the materials you need.

When you buy a piece of land, you know the total size of it in square feet. Your constructor or builder plans the whole house for you, dividing the total available area across your home. They do so by using the quadratic equation.

The size of land, number of rooms, etc., are known factors (like a,b), while the size of rooms and space allocation for stairs or corridors are unknown (the ‘x’). Now, put these values to the equation ax2+bx+c= 0, and you have all the data you need.

2. Running a business? How much profit are you making?

To calculate the profit you earn or are likely to earn from your business, you need the quadratic equation’s help. Whatever product or service you sell, you know how much it costs to produce. You are also aware of the amount of profit you aim to make.

So, you might wonder what your product should be priced at. This unknown selling price is your ‘x’ of the quadratic equation. The cost price and the profit are known factors, ‘a’ and ‘b.’

Now that you have all the elements of a quadratic equation solving it step by step will give you the selling price.

3. How much speed do you need? Estimate with quadratic equations.

Calculating the required speed calls for the use of a quadratic equation. You will find it even more helpful if you are on your college or university rowing team. If you are going upstream, you have to row against the stream.

But you need to know how fast you should row or what should be the speed of your boat. You can easily recognize that by using the quadratic equation. Let’s first look at the known factors. You know the distance you have to row to and back, the speed of the stream, and the total time available to you.

Assuming your speed is ‘x,’ you can put these known values in the ax²+bx+c= 0 equation. Now continue to solve it step-by-step; you will have the answer ready in no time.

4. Are you into sports? You need quadratic equations too!

Velocity quadratic equations are something that athletes and sports analysts use every day, every moment, especially in the case of basketball, javelin throw,  shot put, etc., which involves throwing balls or spears or other such items.

In a basketball team, you will see that one player throws the ball to another, reaching them in a moment after or before they catch it. It will feel like the player knows when he should throw the ball so that it reaches the other player at the exact time.

It is really a matter of quadratic calculation. Here, the known values of ‘a’ and ‘b’ are the heights, speed of the ball, loss of speed due to gravitational force, etc. The time is unknown to you, and this is the ‘x.’ Thus, you can solve it by referring to the ax²+bx+c= 0 equation. This is how your favorite basketball players score.

5. Use of quadratic equations by engineers

Among all the professions, engineers probably use quadratic equations most extensively. Here’s a list:

• Engineers in the automobile industry use quadratic equations to design vehicle structures, especially those with curved patterns.
• Automobile engineers use quadratic equations for designing and installing brake systems.
• Aerospace engineers use these equations for calculating a vertical plane projectile. Calculating the height and velocity of an object when thrown or launched in space, they use the ax²+bx+c= 0 formula to recognize how much time it will take to reach the destination.
• Using complex systems at the workplace calls for regular and frequent use of quadratic equations by electrical and chemical engineers.
• Audio engineers also use quadratic equations to design sound systems to ensure the listeners experience the best sound quality.

6. Satellite dish setting and signal transmission

You need to put up a satellite dish at a particular angle to receive the most efficient signal transmission. The dish on your roof catches the signals from two or more satellites simultaneously and transmits them to your TV through a feed horn.

This whole transmission process involves using quadratic equations to identify the most efficient angle.

7. Use of quadratic equations in defense and military services

We already told you how to use quadratic equations to measure height, distance, speed, etc. These measurements are also used in defense services and military activities.

For example, if the military needs to throw artillery to destroy an enemy camp, they calculate the distance and the speed of launching the artillery through quadratic equations.

8. Do you wish to have a farm? Even then, you need quadratic equations.

At first, agriculture, farming, and quadratic equations might seem like two entirely different topics, but a successful agricultural venture involves quadratic equations.

These equations are used to calculate the total available area and determine how the area will be divided and how crops should be allocated. Randomly building a pen anywhere on the farm will not help you achieve high yields.

The use of quadratic equations ensures agricultural efficiency.

9. Application of quadratic equations= Effective management

In any industry, there are various levels of management. A Production Manager supervises the product line manufacturing and other relevant activities. Again, an Engineering Manager supervises the machinery, work efficiency, etc.

To estimate all these, they take the help of quadratic equations. The Human Resource Managers determine the workforce capability, requirement of recruits, etc., by considering the available work as the known variable.

Thus, management also applies quadratic equations quite unknowingly.

10. Other real-life applications of quadratic equations

In addition to the above examples, there are other real-life instances where quadratic equations are used. These include:

• Astronomers identify and describe solar systems, planets and their orbits, and galaxies with the help of quadratic equations.
• Computer engineers ease the use of complex systems through quadratic equation implementation.
• Criminal investigators determine the trajectories of bullets by using quadratic equations.
• Insurance agents design plans and models through the computation of data. These plans, in most cases, are unique to each consumer. Such a complex process requires in-depth quadratic equation calculation.
• If there is a car accident, quadratic equations help determine car speeds.
• In Physics, different motions are described easily with quadratic equations.
• Chemical Engineers or Chemists working in fields of Chemistry use these equations to describe specific chemical reactions, identify their equilibrium, etc.

Wrapping up

Quadratic equations help us evaluate the relationship between variable quantities. Right from calculating area, speed, and profits to astronomy and criminal investigations, this math concept is useful in every sphere of life.

The above examples clearly show how we use quadratic equations in our daily lives. Therefore, developing a thorough understanding of the subject is necessary if we don’t wish to get stuck finding answers to our everyday queries.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post 10 Real Life Applications Of Quadratic Equations appeared first on Number Dyslexia.

However, when the teachers or parents introduce and give examples to the students as to where it is used in real life, their approach towards the topic would be positively impacted. Hence. Here are some real-life examples of place value that can give insights to students as to where this concept is used practically. 

Place Value: Where is it used in real life? 

There are plenty of math concepts that are consciously and unconsciously used in our daily lives; similarly, place value is as relevant and essential in everyday life as it is in arithmetics. Following are some real-life aspects that can not be maneuvered without an understanding of place value.

1. Time

Time is one area that would make no sense if one cannot understand what value the digit represents. For example, if the time is 3:30 PM, it translates into 3 hours and 30 minutes. Both the digits are 3 but hold a completely different value. If they were considered to be of the same value and not understood by their place in the systems of the time, it would be nearly impossible for people to live at the same time and keep its track.  

2. Calendars

In the absence of knowing place value, calendars would become hard to comprehend. Years, months, weeks, and days, all overlap with the same digits. The date 29/07/2022 represents the 29th day of the 7th month of the year 2022. The 2 in 29 and the 2 in 2022 hold completely different meanings. This would impair understanding of days and events of the past and future. All one would be left with is- today, tomorrow, and yesterday. This way, living and performing basic tasks will become difficult. 

3. Scores

Scores and place value are similarly connected. Scoring 7/100 and 70/100 is completely different. Understanding place value would here mean getting a score of 7 out of 100 and 7 tens out of a hundred. 

4. Finances

Place value has a very important role to play when it comes to our financial affairs of daily life. Paying bills, reading the price tags, and maintaining any kind of finances requires a clear understanding of place value. Imagine walking into a store and reading the retail price for some groceries, to be 25 rupees and 42 rupees. Now, in this case, if a person does not understand how many tens and ones the digits represent, it is nearly impossible for them to pay for it and buy it. Some assumptions may include 2 and 5 rupees separately or 4 and two rupees. This will be done without having a thorough understanding of how 25 means 2 tens and 5 ones, and 42 means 4 tens and 2 ones. 

5. Distance

Without an understanding of place value, simple things like board signs showing a place is, for example, 50kms away, or turn right after 5.2kms, will seem ambiguous and lead to misdirection. 

Conclusion

Place value means the value a digit represents. Having explained how place value is not just a part of mathematics but also of our daily lives, it can be said that moving ahead with a normal life can get strenuous. To make the smallest decisions like waking up at a certain time, buying a packet of chips, paying the bill at a restaurant, or choosing a particular route for travel, one requires clarity and a hands-on understanding of place value. No matter how much one is assisted by the other, it seems vital for every individual to have a clear understanding of place value to lead go about their general chores on a daily basis.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post Importance Of Place Value Concept In Our Daily Lives appeared first on Number Dyslexia.

This can be achieved with admirable interpretation skills. But, what exactly are interpretation skills? To answer all of these questions, we here come with a detailed guide to interpretation skills, strategies to improve it, and examples to make you clearly comprehend the essence behind it.

What are interpretation skills?

By definition, interpretation skills are the ability of an individual who can appropriately discover, determine, and discern the right meaning of the information. These texts can be of any form: documents, messages, charts, tables, graphs, etc. looking into it in detail, it is not only about comprehending the information, here are some other basic skills required to be a good interpreter:

1. Perception – Perception is divided as the sensory function in our brain where the information that is received is organized and interpreted, and the way it leads to our actions leads to the information that is received. To ensure this trait, a supporting environment may also play an important role.
2. Decoding- The decoding procedure is how the brain reads a collection of words or words separately. With decoding, we use our skills to interpret the written language and also the non-verbal gestures. Body language affects the way our brain processes information.  Here the usage of linguistics while interpreting also helps in assessing the information including the knowledge.
3. Recording–  Recording is the act of the brain whereupon receiving the information the brain’s memory is stimulated in a way they can say out about the same later when asked. Here the interpreter’s memory plays a huge role where the comprehension comes into notice and is two-fold which is mental and written.
4. Encoding– This is the method of re-establishing the decoded and recorded information in the brain. Accordingly, it is important for long-term memory retention. This comes after the above three procedures to store information in an efficient way.
5. Listening skills- Interpretation skills are not only constrained to grasping information on paper but also properly understanding verbal lectures and other snippets of information. To ensure better interpretation skills, listening skills with language knowledge in three levels: grammar, syntactic, and contextual patterns are needed. There are several components in these skills like redundancy and active and passive listening. One needs to apply necessary traits when needed. 
6. Emotional Quotient: To understand the piece of text, the learner needs to ensure better empathy to connect with the presentation. Being in the best emotional state possible helps in better interpretation.

Attributes of interpretation skills 

Comprehending the importance of Interpretation skills, let us here look into what attributes are needed to develop these abilities in individuals:

1. By using the recording skill the brain is able to organize and record what is said and the right message is conveyed between the speaker and the interpreter with little to no mistake.
2. Good knowledge of the language: An individual should have a gripping knowledge of the language- its grammar, and other traits; to make sure they comprehend appropriately.  
3. Memory skills: A person should have a specific ability to record the content in their brain and simultaneously collect the same back when needed. For this one may need better memory skills. With focus, one can increase retention abilities. 
4. Intuitive Skills– When the brain has got new information and has to interpret the information at that very moment gives the brain to be alert and gives the upper hand to be prepared in situations like these.  
5. Neutrality– It is the ability of the interpreting person to avoid themselves to incline to either side while comprehending the information. Staying neutral can make them maintain a better attitude in the workspace thereby retaining healthy relationships.

Strategies to improve interpretation skills 

Opting for a style or strategy of the interpretation skill during learning or any other phase can bring about better results effortlessly. The strategies not only will help understand complex themes of long or short texts but also make out what comes next at higher levels. The concept of interpretation skills was addressed so that one can interpret the text or the information received in your own language and not have to consult a book or a person every time one needs to interpret.

Here are a few working strategies that can improve interpretation skills in an individual:

• Making a habit of taking notes. The first step is grasping information, but retaining it for longer durations can be arduous. A habit of making short notes can be a good idea for not only documenting the ideas but also ensuring great writing practice. 
• Form an easy style of remembering. Understanding and remembering the information traversed is important. The individual can opt for strategies like mnemonics, symbols, or easy figures to make information simple to remember. 
• Understand the culture and intent of the information. Based on the context and scenario, the idea behind a piece of information may change. A learner before interpreting a text can make sure of the background of it to better understand the essence.
• Make use of multisensory sources. If the information on a piece of paper is not enough, the learner may look into options like videos, images, or any other multisensory sources to get multiple insights into the same concepts. 
• Try different types of interpretation styles. One may choose among multiple styles of interpretation to see which of these is fitting. Here, let us look into these styles in detail:

1. Literal interpretation is basically asking to give the “who” and the “why” of the text. In this strategy of interpretation, the text is taken as it is and there is nothing metaphorical or symbolic about the text. 
2. Symbolic Interpretations– Sometimes symbolic presentations speak better than visuals, inferring themes is an important tip for learners.
3. The stylistic interpretation is where the text describes the setting, the background where it’s set, and how it will affect the situation in which the text is going ahead. 

Interpretation skills in real-life

As we have seen, Interpretation Skills are not specific to any one topic,  and these help in determining what the message is trying to imply. Let’s have a look at the interpretation skills that are used in real-life occupations and situations.

1. Interpreter as a Diplomat: Diplomats are the people who represent their country abroad. Their duties are to ensure efficient communication with locals and interpret the information that they receive. They need good interpretation skills to perfectly retain what the authorities communicate to smoothen the relationships.
2. Translator: Interpretation Skills can be used by translators while they translate the works of individuals from another language to a language the translator has knowledge of.
3. Like a Radiologist: In departments like Radiology, the interpretation of information from tests, seniors, and also from peers at workstations is important. Sometimes, non-verbal gestures also need to be grasped appropriately to ensure no errors happen. This implies that the candidates and aspirants are obligated to have better interpretation skills. Research by Kevin E’ O Brain^[1] showed that around 81 percent of people they experimented with marked that interpretation is important in radiology. 
4. Students in the classroom: While the learners read textbooks and information from other resources, they interpret the information appropriately to put it on paper for tests.
5. Data Analysis: Professionals like statisticians and other big data handlers not only focus on preparing the final drafts of the data but also interpret them to understand and comment on the trends, statistics, and other crucial information. 

Concluding thoughts

Interpreting a piece of text or document requires certain interpretation skills. These are employed not only in the classroom but also in other industries by professionals. It is important to understand that these skills are not only important for analyzing text information but also for verbal and non-verbal communication. The ability to interpret is often underestimated, but mastering these abilities can make a person strong in discerning information. 

References:

1. O’Brien, K. E., Cannarozzi, M. L., Torre, D. M., Mechaber, A. J., & Durning, S. J. (2008). Training and assessment of CXR/basic radiology interpretation skills: results from the 2005 CDIM Survey. Teaching and learning in medicine, 20(2), 157-162.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

The post Interpretation Skills: Importance, Examples, Strategies, & Real Life Applications appeared first on Number Dyslexia.

Sometimes, learning from real-life cues may be beneficial as the students may ensure better attention to detail. To assist pupils in learning positive and negative numbers, we have listed ten real-life applications that you may have been thorough but have not noticed the implications of these numbers. 

Why is there a need to learn about positive and negative numbers?

We use multiple positive and negative numbers applications every day. Understanding the sign is often crucial in pivotal fields like aviation, shipping, stocks, transportation, and understanding statistics. A small sign mistake can create a blunder that can cause a significant impact. Accordingly, students may need to know the reason “why do these numbers exist?” and “What are the applications of these positive and negative numbers?

What is the idea of positive and negative numbers?

Numbers indicate the quantity or value. The positive and negative may be the indications of addition or subtraction. If a quantity increases, we say that a particular amount of thing has been added to the previous quantity or vice versa if it decreases. The negative number simply shows the decline from the previous state or value, and the positive number shows the increment in the previous state or value. E.g.-  The annual growth percentage in a country’s GDP might be negative, which indicates a recession.

Here are a few advantages of positive-negative numbers:

1. We can detect a wider range of temperatures even below zero degrees which helps us do many chemical reactions which require negative temperatures.
2. The accurate measurement of  elevations helps flights to operate at a safer distance in the sky. (1000 ft apart)
3. Time Zones across the globe are decided by adding or subtracting hours from the GMT.
4. Determining the focal lengths of optical lenses for a clear vision.
5. Positive- Negative polarization helps the charge to flow, resulting in electric current.

Talking beyond the theoretical part, we experience some real-life examples where we use the concept of positive and negative numbers daily without even realizing it. Here are the 10 real-life discussions that depict the value of positive and negative numbers. 

Where we use positive & negative numbers in real life?

Numbers, be it positive or negative are evident almost everywhere around us. We may not notice them but their significance in these few areas is very crucial. Here are a few real-life instances that may assist you in identifying:

1. Stock Exchange

The stock market is an exchange where you can buy or sell the stocks of listed companies. It is the hub of financial activity in an economy. The estimations and depiction here encompass both positive and negative numbers.

Every second, the indices value fluctuates, showing the trend to be positive or negative. The positive integer indicates the growth in the stock prices, while the negative sign means a decline in stock prices.

Your profit and losses are also settled in the form of positive and negative signs. For example, if the price of a stock is $100 and the next day it goes up to $110, the stock is considered positive with a 10 percent increase.

2. Temperature Measurement

The measure of temperature may be a noteworthy example in everyday life where we use positive and negative numbers. Weather reports show if the temperature of a place is high or low in terms of positive and negative signs before putting the numeric value of the temperature.

Countries near the equator have higher temperatures, while nearby poles go beyond zero. The negative temperature is a clear indicator of temperature below the freezing point. For instance, the UAE’s temperature is 45°C which indicates it would be a hot climate there. On the other hand, the temperature of the Arctic region is -25°C, which means it would be cold.

3. Elevation

Elevation indicates the distance from sea level. In simple terms, it means how high or low the object is from the top of the seafloor. Consider Sea level as the origin of the elevation number line, just as 0 is the origin of the counting number line.

As the elevation climbs above sea level towards the sky, numbers rise into the positive. As elevation falls below sea level, numbers fall into the negatives. Though elevation can be negative, it is written as ‘X ft below sea level’ instead of -x feet of elevation. 

4. Latitude & Longitude

Latitudes and longitudes are crucial geographical reference lines. Latitude tells how far north or south of a place’s equator, while longitude tells how far east or west of the Prime Meridian. It is based on Earth’s latitude and longitude grid system, which divides the globe north-south into two zones and east-west into four zones. The grid system allows travelers to find their way from point A to B.

Imaginary Latitude and longitudes lines were drawn around the earth’s surface to be defined as an exact location. The middle of the earth was defined as the equator or 0 degrees. The North Pole is denoted at 90° & South Pole is denoted at -90°. Hence, the latitude shown in the northern hemisphere has positive values while latitude values are negative in the southern hemisphere. Longitudes range from 0° at the prime meridian that runs through London, UK, to ±180° at the antimeridian in the Pacific Ocean. 

5. Lifts (Elevators)

We use elevators every single day. It is a vertical transportation medium that helps us move between multiple stories/ floors of a building. Here, the ground floor is labeled as zero. While the top floors are marked as 1,2,3, the basement and parking are generally marked as -1, -2, and-3, and so on.

Witnessing these in most public places and buildings is one common everyday example we come across using positive and negative numbers.

6. Bank Statements

When you check your Bank Statements or transactions, some transactions have + signs in front of them while others have – sign. The positive sign indicates that the money is deposited or credited into the account. On the other hand, a negative sign indicates a debit, i.e. the money has been sent to someone else.

For simple understanding, the credited money or interest is denoted by a plus sign, and a negative/minus sign denotes debits and charges. Traversing through a bank statement, one can effortlessly observe these figures. 

7. Understanding Statistics 

We need to study the positive and negative integers to conclude a particular result from statistical data. For example, the Calculation of the total population in a particular country will require an estimation of the Immigrants, Emigrants, and consistent population. Then, we need to add up the immigrants and consistent population and subtract the emigrants from it. Officials may need to add up the negative and positive populations to do population calculations and make policies for your country. 

8. Sports

Many indicators in sports events require displaying the negative terms.

• In baseball, the run differential is negative if the team gives away more runs than they have scored themselves.
• Yard gain in football can be positive or negative.

• Formula 1 drivers may be given a time for the lap or sector, such as a record lap or lap just completed. The number is positive if the driver completed the lap at a slower pace and negative if at a faster pace.
  

9. MCQ Exam scores (with negative marking)

MCQ exams are usually a way to assess the knowledge of a subject. Some of these tests may reduce marks for every wrong answer as well.  Consequently,  students may score a negative number as well.  So, the total of negative marks exceeds the positive marks, and then the net score gain becomes a negative score. It can be an unfortunate event for a student. 

10.  Music Charts Ranking – Billboard/ Spotify Rankings

Music Charts or Videos rankings are posted on Billboard every week. The rank gain is denoted by a plus sign in front of the song. The integer value denotes how many ranks the song has come up. If a song goes down in ranking, you can see the negative sign beside the song with an integer that illustrates that the song’s rank has decreased.  

Wrapping up,

There is a growing need to understand positive and negative numbers because they are essential in mathematics, engineering, business, aviation, and other related fields. In addition, positive and negative numbers are important because they allow for comparisons and diversification of numerical data. Negative Numbers often complete the depiction of various quantities.

While there are multiple real-life applications, we have listed the most common choices that many people may have witnessed. Check out these to inculcate your little one’s importance of positive and negative numbers. 

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’, 

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